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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:35"/><i><font color="Green">E30</font></i>: 
( 2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  )
 ;<br/>

<a NAME="E2:35"/><b>then </b><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="topreal1.html#V2">unfolded</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="topreal1.html#V3">s.n.c.</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="topreal1.html#V1">special</a> )
 
<b>by </b><i><a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  <a href="funct_1.html#V2">one-to-one</a> <a href="topreal1.html#V1">special</a> <a href="topreal1.html#V2">unfolded</a> <a href="topreal1.html#V3">s.n.c.</a> <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="jordan3.html#E1:35"><i><font color="Green">E30</font></i></a>, <a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:35_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1"><b>case </b></a><a NAME="E1:35_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:35_1_1_1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 <b>by </b><i><a class="txt" href="jordan3.html#E1:35"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_2"><b>case </b></a><a NAME="E1:35_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:35_1_1_2"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 <b>by </b><i><a class="txt" href="jordan3.html#E2:35"><i><font color="Green">E31</font></i></a>, <a class="ref" href="finseq_1.html#T79">FINSEQ_1:79</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E5:35"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V2">unfolded</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V3">s.n.c.</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V1">special</a> )
 
;<br/>
<b>hence </b><a NAME="E6:35"/>
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>2</sub></font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a> 
 <b>by </b><i><a class="ref" href="topreal1.html#D10">TOPREAL1:def 10</a></i>;<br/>


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